Treee

Treee is a language created by Octogeddonling (talk) 08:49, 4 January 2023 (UTC) . It replaces all letters in lambda calculus into trees of brackets and adds some mess to turn the entire code into uncomputable gibberish.

Grammar

• call all the following an "operation"
• suppose the object have the form(another object...another object) and () is an object
• if the object has form(()followed by at least 3 objects), delete the outer bracket of second and third object, then replace every first object in the second object with the de-bracketed third object, than delete the first (), first object and third object's entirety.
  • for example, (()()(()(()))(()()(()(())))) outputs itself.
  • this step is edited 3 times to actually create a quine
• if the object has form(((()))followed by at least 1 object), delete the first 2 objects in the outermost bracket and prints a character whose ASCII code is equal to the total number of pair of brackets in the second object
  • for example, (((()))(((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))) prints a space and outputs ()
  • for any given number of spaces, just repeat the code above in the same trunk
• if the object has form(((()()))followed by at least 3 objects), then if an operation to the first input ultimately halts and returns a tree with no branches, then the first four is replaced by just the second, otherwise the third object.
  • for example, ((()())A(()()(()(()))(()()(()(()))))(())) reverses the halt for A. This can be used to create a paradox but it's not computable anyway
• the form((()()())followed by at least 3 objects) works in a similar way but instead of checking the halting problem it will check any paradox in the first input. Replace the first four with the second if it's well-founded and return the third if it's not.
• repeat the 4 actions until nothing can be done
• scan all objects in this layer with an operation followed by an operation of this layer each time. For example if A turns into a, than the operation of (Abcd)operates(Abcd), then operates A, then operates (abcd), then operates b
• halt and output if really nothing can be done here

Numeric Form

you can rewrite the whole code into numbers, such as (()()(()(()))(()()(()(())))) to 4 0 0 2 0 1 0 3 0 0 2 0 1 0. now you can write an interpreter of no action 3 and 4 using just Brainfuck!

Version 2

• Version 2 is a simplification to the original one
• the fourth transformation is omitted
• let the transformation of (()A(B)(C)E) be:
  • if A reduces to a tree without branch, aka () (()) ((()))..., the result would be (((B))E)
  • else, the result will be (BC(C)E)
  • if the operation above triggers a paradox, the result would be (((C))E)
• the trigger for printing is (()) now

Version 3

• Version 3 is easier to understand and it is Turing complete anyway
• The form of an operation is (()(A)(B)(C)D), as it in version 1
  • if (A) reduces to a tree without branches, then the result would be the same as it in version 1.
  • else, the result would be the same as (()(A)(B)((C))D) in version 1. There is an extra bracket on C.
  • A paradox will output (BD).
• The form of a printing is ((())(A)B), of which it prints a Unicode character of number of brackets in A.
  • that makes it compatible with other languages

Miscellaneous

This language is uncomputable because obvious.

This language was inspired by SKIΩ calculus and it is supposed to have strength comparable to Xi_2 function.